two higgs doublets from fourth generation condensation · gustavo burdman university of s~ao paulo...
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Two Higgs Doublets from Fourth GenerationCondensation
Gustavo Burdman
University of Sao Paulo
With Carlos Haluch, , arxiv:1109.xxxx
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Outline
Introduction and MotivationIs a Fourth Generation still allowed ?What is it good for ?
Two Higgs Doublet Model from Fermion CondensationEffective TheoryScalar SpectrumPhenomenology
Conclusions
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Is a Fourth Generation Still Viable ?Higgs must either be:
I Lightmh < 120 GeV
I Heavymh > 600 GeV
[GeV]Hm200 300 400 500 600
SM
σ/σ
95%
CL L
imit o
n
210
110
1
10Observed
Expected
σ 1 ±
σ 2 ±
ATLAS Preliminary
1 Ldt = 1.02.3 fb∫
= 7 TeVs
CLs Limits
Generation Modelth
4
Heavy quarks must be mt′ > 450 GeV, mb′ > 400 GeV
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Possible Ways Out
I Dynamical explanation for mh > 600 GeVI Fermion Condensation with low cutoff → Heavy Higgs/No
Higgs
I One Higgs doublet always mh > 700 GeV
I More complicated scalar sectorI Fermion condensation → Two-Higgs doublets at low energy
I (Mostly) heavy scalar spectrum with different σ × BR
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Why a Fourth Generation ?
Heavy Chiral Fermions: strongly coupled to EWSB sector
I Top quark:mt ' v ⇒ yt ∼ 1
I If Heavy Fourth Generation ⇒ y4 > 1
Higgs sector is strongly coupled
I Natural to assume composite Higgs sector
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Why a Fourth Generation ?
Other motivation: (Holdom, Hou, Hurth, Mangano, Sultanasoy, Unel ’09 )
I New CP violation source for baryon asymmetry
I New sources of CPV in meson decays
I · · ·
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Electroweak Symmetry Breaking
Composite EWSB Sector:
I Technicolor: Asymptotically free, unbroken gauge interaction
⇒ 〈FLFR〉 6= 0 ⇒ EWSB
F ’s are confined fermions, just as quarks in QCD.
I Alternative: gauge interaction spontaneously brokenat Λ ∼ 1 TeV⇒ F ’s un-confined heavy fermions with EW quantum #’s(E.g. Bardeen,Hill, Lindner ’90, Hill ’91)
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EWSB from Fourth Generation Condensation
Ingredients:
I A Chiral Fourth Generation: Q4,U4R ,D4R , L4,E4R ,N4R
I New strong interaction at the O(1) TeV scale:
I E.g. Broken gauge symmetry M ∼ TeV
I Strongly coupled to 4th gen. ⇒ 〈F4F4〉 6= 0
⇒ m4 ' (500− 600) GeV
I Other fermion masses: higher dimensional operators like
xijΛ2
f iL fjR URUL
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Models of Fourth Generation Condensation
All ingredients present in AdS5
(GB, Da Rold ’07, GB, Da Rold, Matheus ’09)
Extra dimensional theories in compact AdS5 dual to stronglycoupled theories in 4D:
I Naturally results in strongly coupled heavy fermions
I Higher-dimensional operators among light fermions suppressedby large UV scale Λ
I Build gauge theory in AdS5 with one extra chiral generationand no Higgs .
I Minimal model: Only up-type 4G quark condenses
⇒ Only 1 Higgs doublet, mh ∼> 700 GeV
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Models of Fourth Generation Condensation
I More general and more natural: both up and down typequarks condense
I More natural: interaction must be nearly isospin invariant toavoid T parameter constraints
I More general: would need to fine tune interaction to avoidone condensation
I ⇒ Two Higgs doublets at low energy
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A Two Higgs Doublet from Fermion Condensation
(Luty ’90, Luty, Hill, Paschos ’90, GB, Haluch ’11)
New fermions
Q i =
(U i
D i
)L
, U i , D i
with i gauge index of new interaction.
New Strong Interaction:
I Want un-confined fermions ⇒ spontaneosly broken at scale M
I Massive bosons strongly coupled to Q i , U i and D i
I E.g. If G a color-octect ⇒ i = (1− 3) is color index, Q i , U i
and D i can be fourth-generation quarks
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Electroweak Symmetry Breaking
New strong interactions ⇒ four-fermion operators
L4f =gLguM2
G
QUUQ +gLgdM2
G
QDDQ
with gL, gu, gd gauge couplings. If
gLgu >8π2
Nc⇒ 〈QU〉 6= 0
gLgd >8π2
Nc⇒ 〈QD〉 6= 0
One doublet condensing ⇒ SU(2)L × U(1)Y → U(1)EM
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EWSB and Low Energy Scalar Spectrum
Four-fermion interactions ←→ Yukawa interactions
Leff. = YU(QΦUU + h.c.) + YD(QΦDD + h.c.)
−M2GΦ†UΦU −M2
GΦ†DΦD
with
Y 2U = gLgu, Y 2
D = gLgd , ΦU = −iσ2Φ∗U
with hypercharges hU = −1/2, hd = 1/2.
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EWSB and Low Energy Scalar Spectrum
At µ < MG :
I Scalars develop kinetic terms
Lkin. = ZΦU(µ)(DµΦU)†DµΦU + ZΦD
(µ)(DµΦD)†DµΦD
with the compositness BCs ZΦU(MG ),ZΦD
(MG ) = 0.
I They get VEVs if four-fermion couplings super-critical:
〈QU〉 6= 0↔ 〈ΦU〉 6= 0
〈QD〉 6= 0↔ 〈ΦD〉 6= 0
I Effective Two-Higgs doublet spectrum at low energy
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Low Energy Scalar Spectrum
At µ < MG all couplings get renormalized and some generated.E.g. :
YU →YU√ZΦU
, YD →YD√ZΦD
µ2U = M2
G −gLguNg
8π2
(M2
G − µ2)
µ2D = M2
G −gLgdNg
8π2
(M2
G − µ2)
We ca see that m2U < 0 and m2
D < 0 for super-critical couplings
⇒ V (ΦU ,ΦD) with 〈ΦU〉 = vU , 〈ΦD〉 = vD
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ΦU − ΦD Mixing and Peccei-Quinn Symmetry
Theory is invariant under
Q → e−iθQ U → e iθU D → e iθD
ΦU → e2iθΦU ΦD → e−2iθΦD ,
forbids mixing term µ2UD(Φ†UΦD + h.c .) in V (ΦU ,ΦD).
This results in MA = 0
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Instantons Induce MA
Fermionic equivalent of mixing term
Lmix = GUD(QDUcQ + h.c.) , (Q = −iσ2Q)
But this is generated by ’t Hooft fermion determinant (Hill ’95)
Linst. =k
M2G
det[QLQR
]with k ∼ O(1).
⇒ Instantons of new strong interactions responsible for MA
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Scalar Spectrum
Scalar potential generated by fermion loops
V (ΦU ,ΦD) = µ2U |ΦU |2 + µ2
D |ΦD |2 + µ2UD(ΦU
†ΦD + h.c.)
+λ1
2|ΦU |4 +
λ2
2|ΦD |4 + λ3|ΦU |2|ΦD |2 + λ4|ΦU
†ΦD |2
Couplings YU , YD , λi , µU , µD , µUD run down by using RGEs
⇒ scalar spectrum
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Running to Low Energies
Solutions for λ1(µ) for MG = 2, 3, 4 TeV
0.0 0.5 1.0 1.50
5
10
15
20
25
Μ @TeVD
ΛHΜ
L
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Scalar Spectrum
A =√
2(Im[Φ0
D ] cosβ − Im[Φ0U ] sinβ
)h =
√2(−Re[Φ0
U ] sin γ + Re[Φ0D ] cos γ
]H =
√2(Re[Φ0
U ] cos γ + Re[Φ0D ] sin γ
]H± = Φ±
D cosβ − Φ±U sinβ
tanβ = vU/vD ' 1. The CP-even mixing is
tan 2γ =µ2UD + (λ3 + λ4)v2 sin 2β/2
µ2UD + λ4v2 cos 2β/2
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Scalar Masses
E.g.: Pseudo-scalar mass
µ2UD =
k v2
2M2G
λ1λ2 cos2 β sin2 β[1− kv2(λ1 cos2 β cotβ + λ2 sin2 β tanβ)/(2M2
G )]
and the pseudo-scalar mass is
M2A = −2
µ2UD
sin 2β
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Scalar Masses
For k = (0.1− 1)
MG = 2 TeV MG = 3 TeV MG = 4 TeV
MA (26-118) GeV (15-59) GeV (10-39) GeV
Mh (548-580) GeV (459-467) GeV (422-425) GeV
MH (651-732) GeV (530-537) GeV (482-585) GeV
MH± (603-719) GeV (495-512) GeV (453-459) GeV
I Heavy (h,H,H±) ' (400− 700) GeV depending on (k ,MG )
I Light A ' (10− 120) GeV
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Phenomenology
I Usual h,H decay channels suppressed in favor of AA, A,Z
I If condensing fermions carry color (4G quarks) →σprod.(gg → (h,H,A)) ' (6− 7) SM values
I If new fermion colorless, no enhancement of σprod.. But scalarspectrum still same.
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Electroweak Precision ConstraintsConstraints in the S-T plot (68% and 95% C.L. contoursParameter space of scalar sector (k,MG ) + fourth generation
-0.2 -0.1 0.0 0.1 0.2 0.3 0.4-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
S
T
L = 2 to 4 TeV
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Flavor
I Dynamics at the high scale introduce higher dimensionaloperators such as
xijΛ2
f iL fjR URUL
I Can always accommodate ΦU only couples to up-type quarks,ΦD only to down-type quarks and charged leptons
I PQ symmetry softly broken ⇒ mixing does not induce FCNCsat tree level
I Loop effects: H± too heavy to give important effects inb → sγ, etc.
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Summary/Outlook
I 4th Generation still not excluded by Higgs searches
I Composite 2HDM with light A and heavy (h,H,H±) is anatural consequence of fermion condensation
I If new fermions carry color:I We will see them soon (mt′ > 450 GeV)I σ(h,H,A) larger than in standard 2HDMI But preferred decay channels are (h,H)→ (A,A), (A,Z )
I If new fermions colorless, unusual scalar spectrum still hint offermion condensation